Effusion Rate Calculator

Calculator

Choose a mode, enter values, then submit. The result appears above this form.

Mode

Tip: Gas with smaller molar mass effuses faster, all else equal.

Gas 1 molar mass (M1)

Used for Gas 1, or the single gas in flow mode.

Gas 2 molar mass (M2)

Required when comparing two gases.

Molar mass unit

Most chemistry tables list g/mol.

Rate ratio (r1 / r2)

Use when you measured effusion rates experimentally.

Time ratio (t1 / t2)

Time to effuse the same amount is inverse to rate.

Pressure (P)

Use absolute pressure for best accuracy.

Pressure unit

Converted internally to pascals.

Orifice area (A)

Small orifice, thin wall, molecular flow.

Area unit

Converted internally to square meters.

Temperature (T)

Higher temperature increases effusion flow.

Temperature unit

Converted internally to kelvin.

Example Data Table

Use these sample molar masses for quick comparisons. Values are commonly used approximations.

Gas	Molar mass (g/mol)	Compare vs N₂ (28 g/mol): r_gas/r_N2	Interpretation
He	4.00	2.6458	Faster than N2
H2	2.00	3.7417	Faster than N2
Ne	20.18	1.1779	Faster than N2
N2	28.00	1.0000	Equal to N2
O2	32.00	0.9354	Slower than N2
CO2	44.01	0.7976	Slower than N2
Ar	39.95	0.8372	Slower than N2

Formula Used

Graham’s law (relative effusion): for two gases at the same conditions, the effusion rate ratio is:

r₁ / r₂ = √(M₂ / M₁)

Smaller molar mass → higher rate.

Equal-amount time ratio: time is inverse to rate, so:

t₁ / t₂ = r₂ / r₁ = √(M₁ / M₂)

Orifice effusion molar flow (molecular flow): an ideal thin orifice model gives:

ṅ = (A · P) / √(2π · M · R · T)

ṅ in mol/s, A in m², P in Pa, M in kg/mol, T in K, and R is 8.314462618 J/(mol·K).

How to Use This Calculator

Select a mode based on your goal: compare rates, compare times, or estimate molar flow.
Enter molar masses in g/mol (or switch to kg/mol if needed).
For unknown-mass modes, provide your measured ratio (rate or time).
For flow mode, provide pressure, orifice area, and temperature with correct units.
Click Submit. Your result appears above the form, under the header.
Use Download CSV or Download PDF to export the inputs and outputs.

Effusion as a kinetic indicator

Effusion is the escape of gas molecules through a tiny opening into a lower-pressure space. When the opening is much smaller than the mean free path, molecular motion dominates. Under those conditions, lighter molecules strike the orifice more often and pass through more readily. This makes effusion a useful diagnostic for comparing gases. In vacuum engineering it also helps estimate leak-related throughput during pumpdown.

Rate comparison with Graham’s law

The calculator applies r1/r2 = √(M2/M1) for two gases at the same temperature and pressure. Enter molar masses and obtain a dimensionless ratio. For helium (4 g/mol) versus oxygen (32 g/mol), rHe/rO2 ≈ √8 ≈ 2.828, meaning helium effuses about 2.8 times faster in matched conditions.

Time ratio for equal amounts

Many lab procedures record the time to release a fixed amount rather than the instantaneous rate. Since time is inversely proportional to rate, t1/t2 = √(M1/M2). This supports comparisons from pressure-drop trials, soap-film displacement, or fixed-volume collection. The output helps report results consistently even when instruments measure time only.

Orifice molar flow estimation

For an ideal thin orifice in molecular flow, the tool uses ṅ = (A·P)/√(2π·M·R·T). Provide area, absolute pressure, temperature, and molar mass. Output is shown in mol/s, mol/min, and mol/hr. Pressure scales linearly, while temperature and molar mass reduce flow by a square-root dependence.

Assumptions and uncertainty controls

Graham’s law assumes identical conditions and near-ideal behavior, so temperature gradients, humidity, or non-ideal mixtures can shift ratios. The orifice model assumes a sharp-edged, short opening and molecular flow; viscous regimes or long capillaries require different equations. Improve reliability by logging units, repeating trials, and averaging ratios across runs.

Reporting and export-ready records

After you submit, the results block appears above the form for quick review. CSV export saves inputs and outputs in a simple three-column structure for notebooks and spreadsheets. PDF export captures the formatted results and the Plotly bar chart for documentation. For audits, note the gas identity, molar masses, and the date of measurement. Use consistent sample labels so exported files trace back to cylinders, regulators, and conditions.

FAQs

1) Why does a lighter gas effuse faster?

At the same temperature, lighter molecules have higher average speeds, so more reach and pass through a small opening per unit time under comparable conditions.

2) When should I use the time ratio mode?

Use it when your experiment measures how long it takes to release the same amount of gas, such as fixed-volume collection or a defined pressure drop.

3) Do I need absolute pressure in the flow estimate?

Yes. The orifice flow equation uses absolute pressure. Gauge pressure can underestimate throughput unless you add atmospheric pressure where appropriate.

4) What conditions can break Graham’s law accuracy?

Large temperature differences, strong non-ideal interactions, significant humidity, or mixtures with changing composition can cause deviations from the simple square-root ratio.

5) Is the orifice formula valid for long tubes?

Not usually. Long capillaries introduce friction and viscous effects. The provided model is for a thin, sharp-edged orifice in molecular-flow conditions.

6) What does the Plotly chart represent?